Module 01: Vectors in Euclidean Space
Module 02: Systems of Linear Equations
Module 03: Matrices and Linear Mappings
Module 04: Vector Spaces
Module 05: Inverses and Determinants
Module 06: Diagonalization
Lecture 1: Vector Addition and Scalar Multiplication (9:31)
Lecture 2: Properties of Vectors in ℝ ⁿ and Spanning (30:01)
Lecture 3: Linear Independence and Surfaces (28:33)
Maple T.A. Practice Problems: Quiz: Vector Addition and Scalar Multiplication
Lecture 4: Subspaces (19:13)
Maple T.A. Practice Problems: Quiz: Subspaces
Lecture 5: Dot Product and Cross Product (10:53)
Maple T.A. Practice Problems: Quiz: Dot Product, Cross Product, and Scalar Equations
Lecture 6: Scalar Equation of a Plane and Projections (11:46)
Maple T.A. Practice Problems: Quiz: Projections
Lecture 7: Systems of Linear Equations (12:29)
Maple T.A. Practice Problems: Quiz: Systems of Linear Equations
Lecture 8: Solving Systems of Linear Equations (18:53)
Optional Lecture: Gauss-Jordan Elimination (7:28)
Lecture 9: Homogeneous Systems and Rank (10:13)
Maple T.A. Practice Problems: Quiz: Solving Systems of Linear Equations
Lecture 10: Matrices (10:25)
Lecture 11: Matrix Multiplication and Properties (21:29)
Lecture 12: The Identity Matrix and Block Multiplication (11:21)
Maple T.A. Practice Problems: Quiz: Operations on Matrices
Lecture 13: Matrix Mappings (8:59)
Lecture 14: Linear Mappings (16:38)
Lecture 15: Geometrical Linear Mappings (8:09)
Maple T.A. Practice Problems: Quiz: Linear Mappings
Lecture 16: Special Subspaces (24:23)
Maple T.A. Practice Problems: Quiz: Special Subspaces
Lecture 17: Operations on Linear Mappings (14:59)
Maple T.A. Practice Problems: Quiz: Operations on Linear Mappings
Lecture 18: Vector Spaces (21:28)
Lecture 19: Vector Spaces and Subspaces (19:48)
Lecture 20: Spanning and Linear Independence (11:06)
Maple T.A. Practice Problems: Quiz: Vector Spaces
Lecture 21: Bases (22:40)
Lecture 22: Dimension of a Vector Space (19:02)
Maple T.A. Practice Problems: Quiz: Bases and Dimension
Lecture 23: Coordinates (12:40)
Lecture 24: Change of Coordinates (14:39)
Maple T.A. Practice Problems: Quiz: Coordinates
Lecture 25: Matrix Inverses (21:39)
Maple T.A. Practice Problems: Quiz: Matrix Inverses
Lecture 26: Elementary Matrices (24:31)
Maple T.A. Practice Problems: Quiz: Elementary Matrices
Lecture 27: Determinants (17:41)
Lecture 28: Determinants and Row Operations (15:24)
Maple T.A. Practice Problems: Quiz: Determinants
Lecture 29: Cofactor Method and Cramer's Rule (11:28)
Maple T.A. Practice Problems: Quiz: Determinants and Systems of Equations
Lecture 30: Area and Volume (10:27)
Maple T.A. Practice Problems: Quiz: Area and Volume
Lecture 31: Matrix of a Linear Mapping and Similar Matrices (19:27)
Maple T.A. Practice Problems: Quiz: Matrix of a Linear Mapping, Similar Matrices
Lecture 32: Eigenvalues and Eigenvectors (14:32)
Lecture 33: Eigenvalues and Eigenvectors Continued (21:46)
Maple T.A. Practice Problems: Quiz: Eigenvalues and Eigenvectors
Lecture 34: Diagonalization Theory (12:43)
Lecture 35: Diagonalization Examples (21:29)
Maple T.A. Practice Problems: Quiz: Diagonalization
Lecture 36: Power of Matrices (10:24)